The generator matrix

1 0 0 0 0 0 1 1 1 X 0 1 1 1 X 1 1 0 1 X 0 X 1 1 1 1 0 1 X 1 1 1 0 1
0 1 0 0 0 0 0 0 0 0 0 0 0 0 X X X X 1 1 1 1 X+1 1 X+1 X 1 1 1 1 X+1 X 1 1
0 0 1 0 0 0 0 0 0 0 X 1 1 X+1 1 X+1 X+1 1 X+1 1 1 X+1 X X 0 X X 1 0 X+1 X+1 1 X+1 X+1
0 0 0 1 0 0 0 1 1 1 1 0 X X 1 1 X+1 0 0 X X X+1 0 0 X X+1 0 X+1 1 X X+1 0 0 X
0 0 0 0 1 0 1 0 X+1 1 1 X 1 0 X X X+1 0 1 0 X+1 X+1 X+1 0 1 0 1 1 X 1 X 1 X 0
0 0 0 0 0 1 1 X+1 X 1 0 0 0 1 1 0 X 1 1 X+1 X+1 1 X 0 X+1 X 1 X X X+1 0 1 X+1 X+1
0 0 0 0 0 0 X X 0 0 X X 0 0 X 0 X 0 0 X 0 X 0 X 0 0 X 0 0 X X X 0 0

generates a code of length 34 over Z2[X]/(X^2) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+80x^25+144x^26+262x^27+374x^28+398x^29+524x^30+572x^31+611x^32+688x^33+735x^34+738x^35+738x^36+684x^37+503x^38+404x^39+293x^40+176x^41+133x^42+70x^43+27x^44+22x^45+9x^46+3x^48+2x^51+1x^52

The gray image is a linear code over GF(2) with n=68, k=13 and d=25.
This code was found by Heurico 1.10 in 1.39 seconds.